6-8 hours before cooking, marinate the black cod. If you feel comfortable that you have very fresh fish, marinade for up to 2 days.
Bring the sake (or sherry), mirin, miso paste and sugar to a boil in a medium saucepan over medium high heat. Let boil for 30-45 seconds to evaporate the alcohol. The miso glaze will turn a caramel color. Remove from heat and cool to room temperature.
Pat the black cod fillets thoroughly dry with paper towels. Slather the fish with the miso marinade and place in a non-reactive dish or bowl and cover tightly with plastic wrap. Leave to marinate in the refrigerator for 6 - 8 hours. For even better results, marinate for 2 to 3 days in advance.
To cook the fish: Preheat oven to 400°F. Heat an oven-proof skillet over medium-high heat on the stovetop. Lightly wipe off any excess miso clinging to the fillets, but don't rinse it off. Coat the cod with a little oil then place the fish skin-side-up on the pan and cook until the flesh of the fish browns and blackens in spots, about 3 minutes.
Flip and continue cooking until the other side is browned, 2 to 3 minutes. Transfer to the oven and bake for 5 to 10 minutes, until fish is opaque and flakes easily.
For the Coconut Rice
Melt the butter in a heavy 4-quart saucepan over medium heat. Add the ginger and garlic, and cook, stirring, until just fragrant. Add the rice and cook, stirring, for 1 minute.
Add the coconut milk, water, salt, sugar, and bring to a boil over medium-high heat. Stir in the lime zest. Reduce the heat to low, cover, and simmer until the rice is tender, about 15 minutes.
Let stand off the heat, covered, for 5 minutes. Fluff with a fork, top with more zest, if you like, and serve.